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Department of Mechanical Engineering ESE Specialist Modules

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Department of Mechanical Engineering


MSc/PGDip/PGCert in Energy Systems and the Environment

Specialist Modules


Monday 17 January 2005
1.00 4.00 p.m.


Full time MSc/PGDip/PGCert Students should attempt
ONE question from each module

Part-time postgraduates and exchange students should attempt
ONE question per module for which they are registered.



Calculators must not be used to store text and/or formulae nor be capable of
communication. Invigilators may require calculators to be reset.




16915/16525 ENERGY RESOURCES AND POLICY

Q.1 (a) In a hydro-electric plant, the power P delivered to the turbines is given by
the expression





=
5
2
2
32
D
Q
L
f
H
g
Q
P
,
where Q is the volume flowrate, is the density of water, H is the gross
head at the site, and f, L and D are the friction factor, length and diameter
of the pipe conveying the water.

Show that P will be a maximum when


H
g
D
Q
L
f
3
1
32
5
2
2
= .


(5 marks) ESE Specialist Modules

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(b)





(c)



(d)
At a site with a head of 290 m, 150 MW is required for the turbines. The
pipe length is 1200 m and its friction factor is 0.006. If the system were run
at its maximum power condition, what volume flowrate of water would be
required? And what diameter of pipe would be necessary?


If the system is in fact constructed with a pipe of 3.5 m diameter, show that
the system will produce 150 MW at a volume flowrate of 55.4 m
3
/s. What is
the system transmission efficiency in this case?

Sketch the power/flowrate characteristic curves for the two cases (for
maximum power operation, and using a pipe of 3.5 m diameter), indicating
the position of the operating point for each.







(8 marks)
(8 marks)
(4 marks)
Q.2
Offshore wind, tidal energy and ocean wave power are renewable sources
which are relevant to the UK. In which of these should we be investing our
technical and financial resources over the next 10 to 20 years? Consider
each resource in terms of such issues as:

future
potential
technical
maturity
security of supply
likely costs, per unit of energy produced

and any other factors which are relevant. Then make some
recommendations for future policy.















(25 marks)






16916/16526 ENERGY SYSTEMS ANALYSIS


Q.3 (a) A horizontal uninsulated steam pipe passes through a large room in which
the air and surfaces are at 18°C. The outside diameter of the pipe is 120
mm and its surface temperature and emissivity are 136°C and 0.92
respectively. Using the tables provided and the information given below,
calculate the heat loss per unit length of pipe by radiation and natural
convection.

For convection,
Nu = 0.53 (GrPr)
0.25

Gr = g (T)l
3

2
/µ
2



For radiation,
= 5.67
×
10
-8
W/m
2
K
4

and


(
)






+
+
=
2
2
2
1
12
1
1
4
2
4
1
1
1
A
A
F
1
1
T
T
A
Q








(10 marks) ESE Specialist Modules

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(b) Lubricating oil flows at a rate of 300 kg/h through a thin-walled 15 mm
diameter tube of an oil cooler. Cooling water flows in the opposite direction
through the annular space formed by this tube and a larger tube. The oil
has to be cooled from 100°C to 70°C. The water enters the cooler at 18°C.
The water flow rate is 240 kg/h. The heat transfer coefficient between the
oil and the tube is 400 W/m
2
K

and between the tube and the water is 1270
W/m
2
K. Using the information given below, determine:

i) the required length of the cooler

ii) the effectiveness of the cooler.

specific heat of oil =
2.32 kJ/kgK


specific heat of water =
4.18 kJ/kgK

















(10 marks)

(c) Air has a dew point temperature of 10°C, an enthalpy of 39.61 kJ/kg d.a.
and a total pressure of 100 kN/m
2
. Using the tables provided, determine
the dry bulb temperature and the relative humidity.





(5 marks)

Q.4 (a) A gas turbine plant consists of one compressor stage, a combustion
chamber and two turbine stages. The HP turbine drives the compressor.
The LP turbine provides the power output from the plant. The air enters the
compressor at 1 bar, 20°C. The inlet conditions to the HP turbine are 9
bar, 650°C. The isentropic efficiencies of the compressor, HP and LP
turbines are 0.81, 0.85 and 0.83 respectively. Determine:

i) the pressure and temperature at inlet to the LP turbine

ii) the specific net work output, work ratio and thermal efficiency

Assume air is the working fluid throughout with

= 1.4
and

C
p
= 1.005 kJ/kgK




(15 marks)

(b) An ammonia vapour compression refrigeration plant operates with two
stages of compression between condenser and evaporator pressures of
1250 kN/m
2
and 200 kN/m
2
respectively. The pressure ratio is the same for
each stage and both compressions can be taken as isentropic. The system
uses two stages of expansion and incorporates a flash intercooler
operating at the interstage pressure. The refrigerant is dry saturated at
entry to both compressors and leaves the condenser undercooled to 20°C.
Sketch the plant layout and, using the p-h chart provided, determine the
coefficient of performance of the system and the effective swept volume of
the HP compressor in m
3
/min per kW of refrigeration capacity.




(10 marks) ESE Specialist Modules

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16917/16527 ELECTRICAL POWER SYSTEMS


Q.5
The basic equivalent circuit for one phase of a synchronous motor is as
follows:




(a) Using the diagram prove that the power delivered from the motor is equal
to: sin




=
s
X
E
V
P



(6 marks)

(b) An eight pole, three phase motor is rated at 1MW. If the efficiency of the
motor at rated power is 90%, the power factor is 0.9 lagging, the voltage is
13.2kV (phase-phase), the synchronous reactance is 50 and the grid
frequency is 60Hz calculate:




i) the rotational speed

(2 marks)


ii) the rated torque

(2 marks)


iii) the armature current

(2 marks)


iv) the excitation voltage and phase angle

(4 marks)


v) the pullout torque


(2 marks)

(c) Outline the main differences between a synchronous generator and an
induction generator, also giving a typical example of where each would be
used.


(4 marks)

(d) A developer plans to install a small 0.5MW hydro scheme in the north of
Scotland. The turbine for the scheme is designed to run at 150rpm with a
synchronous generator featuring a salient pole rotor.




i) explain why a salient pole rotor is used

(2 marks)


ii) calculate the number of poles required if the grid frequency is 50Hz





(1 mark)
o
V 0

o
E X
s
ESE Specialist Modules

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Q.6 (a) Between 1990 and 2004, the percentage of UK electricity supplied by gas
fired power stations increased from less than 1% to more than 30%, largely
displacing coal power stations. With reference to emissions and efficiency,
explain why gas power stations are more attractive than their coal
equivalents.

(8 marks)

(b) A 4 pole, three-phase, 12kW induction motor powers a fan in a power
station ventilation circuit. The pump operates at 1440 rpm, 440V, 50Hz and
frictional losses are 600W. Calculate:



i)
the
slip

(1 mark)


ii) the mechanical power developed

(2 marks)


iii) the torque developed by the motor

(1 mark)


iv) the air gap power

(2 marks)


v) the rotor copper loss


(2 marks)

(c) If motor of part (b) is star connected, calculate the neutral current if the
power supplied is equal across all three phases and explain your answer.

(2 marks)

(d) Describe the two main philosophies for power systems protection,
explaining the basic principle of operation of each.

(4 marks)

(e) Power systems protection is essentially a type of systems control: describe
the three main components found in any control system and explain their